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- W4287236871 abstract "In this paper, we investigate Riesz energy problems on unbounded conductors in $R^d$ in the presence of general external fields $Q$, not necessarily satisfying the growth condition $Q(x)toinfty$ as $xtoinfty$ assumed in several previous studies. We provide sufficient conditions on $Q$ for the existence of an equilibrium measure and the compactness of its support. Particular attention is paid to the case of the hyperplanar conductor $R^{d}$, embedded in $R^{d+1}$, when the external field is created by the potential of a signed measure $nu$ outside of $R^{d}$. Simple cases where $nu$ is a discrete measure are analyzed in detail. New theoretic results for Riesz potentials, in particular an extension of a classical theorem by de La Vall'ee-Poussin, are established. These results are of independent interest." @default.
- W4287236871 created "2022-07-25" @default.
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- W4287236871 date "2021-04-08" @default.
- W4287236871 modified "2023-09-23" @default.
- W4287236871 title "Riesz energy problems with external fields and related theory" @default.
- W4287236871 doi "https://doi.org/10.48550/arxiv.2104.03733" @default.
- W4287236871 hasPublicationYear "2021" @default.
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